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U-turn alternating sign matrices, symplectic shifted tableaux and their weighted enumeration

U-turn alternating sign matrices, symplectic shifted tableaux and their weighted enumeration
U-turn alternating sign matrices, symplectic shifted tableaux and their weighted enumeration
Alternating sign matrices with a U--turn boundary (UASMs) are a recent generalization of ordinary alternating sign matrices. Here we show that variations of these matrices are in bijective correspondence with certain symplectic shifted tableaux that were recently introduced in the context of a symplectic version of Tokuyama's deformation of Weyl's denominator formula. This bijection yields a formula for the weighted enumeration of UASMs. In this connection use is made of the link between UASMs and certain square ice configuration matrices.
alternating sign matrices, symplectic tableaux
0925-9899
395-421
Hamel, A.M.
f6d895ef-50b1-4c1c-994f-a6ea3544a715
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706
Hamel, A.M.
f6d895ef-50b1-4c1c-994f-a6ea3544a715
King, R.C.
76ae9fb3-6b19-449d-8583-dbf1d7ed2706

Hamel, A.M. and King, R.C. (2005) U-turn alternating sign matrices, symplectic shifted tableaux and their weighted enumeration. Journal of Algebraic Combinatorics, 21 (4), 395-421. (doi:10.1007/s10801-005-3019-8).

Record type: Article

Abstract

Alternating sign matrices with a U--turn boundary (UASMs) are a recent generalization of ordinary alternating sign matrices. Here we show that variations of these matrices are in bijective correspondence with certain symplectic shifted tableaux that were recently introduced in the context of a symplectic version of Tokuyama's deformation of Weyl's denominator formula. This bijection yields a formula for the weighted enumeration of UASMs. In this connection use is made of the link between UASMs and certain square ice configuration matrices.

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Published date: June 2005
Keywords: alternating sign matrices, symplectic tableaux

Identifiers

Local EPrints ID: 50558
URI: http://eprints.soton.ac.uk/id/eprint/50558
DOI: doi:10.1007/s10801-005-3019-8
ISSN: 0925-9899
PURE UUID: 4bcbf7b2-a49e-48ff-b32b-be07e4f9ba20

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Date deposited: 03 Mar 2008
Last modified: 15 Mar 2024 10:07

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Contributors

Author: A.M. Hamel
Author: R.C. King

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